Explanation Given information : The length of the rod is l . The applied load is P . Show the free body diagram of the thin rod as in Figure (1). Use Figure (1). Determine the distance between AB using the Pythagorean Theorem. A B = ( Vertical distance ) 2 + ( Horizontal distance ) 2 (I) Substitute 2 r for vertical distance and a for horizontal distance in Equation (I). A B = ( 2 r ) 2 + ( a ) 2 = 4 r 2 + a 2 Express the angle θ as follows: tan θ = 2 r a (II) Express the distance ( y ) between point O and B using the similar triangle: 2 r 4 r 2 + a 2 = y + 2 r l 2 r l = y + 2 r ( 4 r 2 + a 2 ) 2 r l 4 r 2 + a 2 − 2 r = y Along the horizontal direction : Apply the equation of equilibrium in the x axis. ∑ F x = 0 P = F B cos ( 90 ° − θ ) (III) Here, the friction force at B is F B . Along the vertical direction : Apply the equation of equilibrium in the y axis. ∑ F y = 0 F A = F B sin ( 90 ° − θ ) (IV) Here, the friction force at A is F A . Determine the distance a needed for equilibrium if the applied load is P by taking the moment about point B , using the equation of equilibrium. ∑ M B = 0 F A × a − P × y = 0 (V) Conclusion: Equation (III) can be written as follows: P = F B sin θ Here, the value of cos ( 90 ° − θ ) is equal to sin θ . Equation (IV) can be written as follows: F A = F B cos θ Here, the value sin ( 90 ° − θ ) is equal to cos θ . Substitute F B cos θ for F A , F B sin θ for P , and 2 r l 4 r 2 + a 2 − 2 r for y in Equation (V)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 5.4, Problem 59P

To determine

The distance a needed for equilibrium if the applied load is P.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.4, Problem 58P

Chapter 5.4, Problem 60P

Students have asked these similar questions

A ship of 8000 tonne displacement floats in seawater of 1.025 t/m3 and has a TPC of 14. The vessel moves into fresh water of 1.000 t/m3 and loads 300 tonne of oil fuel. Calculate the change in mean draught.

Auto Controls DONT COPY ANSWERS - will report Perform the partial fraction expansion of the following transfer function and find the impulse response: G(s) = (s/2 + 5/3) / (s^2 + 4s + 6) G(s) =( 6s^2 + 50) / (s+3)(s^2 +4)

I submitted the below question and received the answer i copied into this question as well. Im unsure if it is correct, so looking for a checkover. i am stuck on the part tan-1 (0.05) = 0.04996 radians. Just unsure where the value for the radians came from. Just need to know how they got that answer and how it is correct before moving on to the next part. If any of the below information is wrong, please feel free to give me a new answer or an entire new explanation. An Inclining experiment done on a ship thats 6500 t, a mass of 30t was moved 6.0 m transvesly causing a 30 cm deflection in a 6m pendulum, calculate the transverse meta centre height. Here is the step-by-step explanation: Given: Displacement of the ship (W) = 6500 tonnes = 6500×1000=6,500,000kg Mass moved transversely (w) = 30 tonnes=30×1000=30,000kg The transverse shift of mass (d) = 6.0 meters Pendulum length (L) = 6.0 meters Pendulum deflection (x) = 30 cm = 0.30 meters Step 1: Formula for Metacentric Height…

Chapter 5 Solutions

Engineering Mechanics: Statics

Ch. 5.2 - Prob. 1P Ch. 5.2 - Prob. 2P Ch. 5.2 - Prob. 3P Ch. 5.2 - Prob. 4P Ch. 5.2 - Prob. 5P Ch. 5.2 - Prob. 6P Ch. 5.2 - Prob. 7P Ch. 5.2 - Prob. 8P Ch. 5.2 - Prob. 9P Ch. 5.4 - Determine the horizontal and vertical components...

Knowledge Booster

The distance a needed for equilibrium if the applied load is P .

The distance a needed for equilibrium if the applied load is P.

Want to see the full answer?

Chapter 5 Solutions